4.5x(x-9)=-13.5

Solution for 4.5x(x-9)=-13.5 equation:

4.5x(x-9)=-13.5

We move all terms to the left:

4.5x(x-9)-(-13.5)=0

We add all the numbers together, and all the variables

4.5x(x-9)+13.5=0

We multiply parentheses

4x^2-36x+13.5=0

a = 4; b = -36; c = +13.5;
Δ = b2-4ac
Δ = -362-4·4·13.5
Δ = 1080
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{30}}{2*4}=\frac{36-6\sqrt{30}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{30}}{2*4}=\frac{36+6\sqrt{30}}{8}
$